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... This section presents the results attained by varying the phase congruency parameters, as suggested in the previous one. The original Kovesi code can be used to evaluate phase congruency in images , as well as an open source application, written by the authors in Java, as an Imagej plug-in , which includes further enhancements for noise estimation , different PC quantization functions  and the use of tile mirror in conjunction with Radix-2 FFT to obtain more accurate edges at the edges of images when at least one side of the image is not a power of two [28,29]. Figures 7-9 show the results obtained by applying phase congruency on the sample images, shown in Figures 7a, 8a and 9a changing the quantization functions to highlight that the modification of the global parameters can be tuned for the same purpose, independent of the quantization function shape. ...
Phase congruency is a technique that has been used for edge, corner and symmetry detection. Its implementation through the use of monogenic filters has improved its computational cost. For this purpose, different methods of implementation have been published, but they do not use a common notation, which makes it difficult to understand. Therefore, this paper presents a unified mathematical formulation that allows a general understanding of the Monogenic phase congruency concepts and establishes criteria for its use. A new protocol for parameter tuning is also described, allowing better practical results to be obtained with this technique. Some examples are presented allowing one to observe the changes produced in the parameter tuning, evidencing the validity of the proposed criteria.
Automatic registration of optical and synthetic aperture radar (SAR) images is a challenging task due to the influence of SAR speckle noise and nonlinear radiometric differences. This study proposes a robust algorithm based on phase congruency to register optical and SAR images (ROS-PC). It consists of a uniform Harris feature detection method based on multi-moment of the phase congruency map (UMPC-Harris) and a local feature descriptor based on the histogram of phase congruency orientation on multi-scale max amplitude index maps (HOSMI). The UMPC-Harris detects corners and edge points based on a voting strategy, the multi-moment of phase congruency maps, and an overlapping block strategy, which is used to detect stable and uniformly distributed keypoints. Subsequently, HOSMI is derived for a keypoint by utilizing the histogram of phase congruency orientation on multi-scale max amplitude index maps, which effectively increases the discriminability and robustness of the final descriptor. Finally, experimental results obtained using simulated images show that the UMPC-Harris detector has a superior repeatability rate. The image registration results obtained on test images show that the ROS-PC is robust against SAR speckle noise and nonlinear radiometric differences. The ROS-PC can tolerate some rotational and scale changes.
At present, many feature descriptors-based registration methods have been proven to be robust in case of complex intensity distortions. However, most of these feature descriptors are only related to intensity information in a patch of neighboring pixels and ignoring the neighbor orientation information, which make the registration performance for medical images with low-resolution appear to be weak robustness and low accuracy. To improve the robustness and accuracy, a novel feature descriptor, named Local-Phase mean and Phase-Congruency values of different Orientations (LPPCO), is developed using filter-bank of Log-Gabor filters at different orientations and frequencies. Next, a similarity measure named LPPCOncc is developed using the normalized cross correlation (NCC) of the LPPCO descriptors, followed by a fast template matching techniques for detecting correspondences between the different images. Additionally, a more sensitivity of phase deviation function is presented for the calculation of phase congruency. The main steps of constructing the similarity measure LPPCOncc include: firstly, we extract the local phase mean and phase congruency values for each pixel in each orientation; secondly, local phase mean orientation histograms and phase congruency values orientation histograms over all the pixels are computed respectively, where the maximum response values are chosen to vote for the corresponding bin; thirdly, combining the two resulting histograms obtains the feature descriptor LPPCO; finally, the LPPCO descriptor is compared across images using NCC. Experimental results show that LPPCOncc is robust to complex intensity distortions between multimodal medical images and outperforms other similarity metrics such as NCC and DLSC. Furthermore, LPPCOncc-based registration algorithm preformed on various types of multimodal medical image pairs shows that it outperforms the NMI-based and DLSC-based registration methods in the registration robustness and accuracy.
To enhance the precision of edge localization and noise suppression in a color image, we propose a conformal monogenic phase congruency model-based (CMPCM) edge detection algorithm that has a good analytical capability in a spatial domain for local structural features to exploit points of the maximum phase congruency in two-dimensional images, and employ Pratt’s Figure of Merit (PFOM) evaluation metrics to measure the performance of its edge detection. Comprehensive experiments were conducted on synthetic color images and natural color images from BSDS500 and LPAICI standard image datasets. The experimental results demonstrated that the proposed CMPCM algorithm outperforms other algorithms, such as viz. Canny, LOG, VPMM, PC and MPC, and has smaller computational time consumption as well.
Local region description of multi-sensor images remains a challenging task in remote sensing image analysis and applications due to the non-linear radiation variations between images. This paper presents a novel descriptor based on the combination of the magnitude and phase congruency information of local regions to capture the common features of images with non-linear radiation changes. We first propose oriented phase congruency maps (PCMs) and oriented magnitude binary maps (MBMs) using the multi-oriented phase congruency and magnitude information of log-Gabor filters. The two feature vectors are then quickly constructed based on the convolved PCMs and MBMs. Finally, a dense descriptor named the histograms of oriented magnitude and phase congruency (HOMPC) is developed by combining the histograms of oriented phase congruency (HPC) and the histograms of oriented magnitude (HOM) to capture the structure and shape properties of local regions. HOMPC was evaluated with three datasets composed of multi-sensor remote sensing images obtained from unmanned ground vehicle, unmanned aerial vehicle, and satellite platforms. The descriptor performance was evaluated by recall, precision, F1-measure, and area under the precision-recall curve. The experimental results showed the advantages of the HOM and HPC combination and confirmed that HOMPC is far superior to the current state-of-the-art local feature descriptors.
When the Discrete Fourier Transform of an image is computed, the image is implicitly assumed to be periodic. Since there is no reason for opposite borders to be alike, the ``periodic'' image generally presents strong discontinuities across the frame border. These edge effects cause several artifacts in the Fourier Transform, in particular a well-known ``cross'' structure made of high energy coefficients along the axes, which can have strong consequences on image processing or image analysis techniques based on the image spectrum (including interpolation, texture analysis, image quality assessment, etc.). In this paper, we show that an image can be decomposed into a sum of a ``periodic component'' and a ``smooth component'', which brings a simple and computationally efficient answer to this problem. We discuss the interest of such a decomposition on several applications.
This paper introduces a two-dimensional (2-D) generalization of
the analytic signal. This novel approach is based on the Riesz
transform, which is used instead of the Hilbert transform. The
combination of a 2-D signal with the Riesz transformed one yields a
sophisticated 2-D analytic signal: the monogenic signal. The approach is
derived analytically from irrotational and solenoidal vector fields.
Based on local amplitude and local phase, an appropriate local signal
representation that preserves the split of identity, i.e., the
invariance-equivariance property of signal decomposition, is presented.
This is one of the central properties of the one-dimensional (1-D)
analytic signal that decomposes a signal into structural and energetic
information. We show that further properties of the analytic signal
concerning symmetry, energy, allpass transfer function, and
orthogonality are also preserved, and we compare this with the behavior
of other approaches for a 2-D analytic signal. As a central topic of
this paper, a geometric phase interpretation that is based on the
relation between the 1-D analytic signal and the 2-D monogenic signal
established by the Radon (1986) transform is introduced. Possible
applications of this relationship are sketched, and references to other
applications of the monogenic signal are given
Phase congruency is an advanced technique for edge detection in images. However, in the original technique, edge detection errors can occur when at least one side of the image is not a power of two. In this paper, this problem, not reported before, and its origin are exposed and two ways of correction are proposed to reduce this problem. The proposed solutions allow to overcome the presented problem by obtaining more accurate and uniform contours than the original technique.
Phase congruency is a relative unknown and powerful image processing technique for segmentation, having been used in diatom image processing, microscopic algae found in water and used to evaluate its quality. However, an important limitation of phase congruence is its sensitivity to noise. To prevent noise from affecting segmentation results, a good noise level estimation is necessary. It can be done with the analysis of the image of local energy. In this paper, we propose the use of the Weibull distribution to estimate the noise profile of the local energy image. The results are compared, in diatom images, with those obtained with the commonly employed Rayleigh distribution and the exponential. The results showed that the Weibull distribution allows a better estimation of the noise level.
The image brightness and contrast changes remain invariant when phase congruency changes. Specifically the monogenic filters, a new image feature detection method is proposed, which is based on phase congruency and the monogenic signal theory in this paper. The performances of Monogenic filters are excelled to that of Log-Gabor filters in theory, hence a greater amount of feature vectors are generated. Compared with the Log-Gabor filters, the most important advantage of Monogenic filters is that it performances with lower time and smaller memory space. The experimental result indicates that image features with Monogenic filters can not only overcome the limitations of Log-Gabor filters, but also improve the location accuracy and anti-noise ability with comparable or better performance.
The frequency domain plays an important role in image processing to smooth, enhance, and detect edges of images. Although image data typically does not include imaginary values, the fast Fourier transform (FFT) has been used for obtaining spectra. In this paper, the fast Hartley transform (FHT) is used to transform two-dimensional image data. Because the Hartley transform is real valued, it does not require complex operations. Both spectra and autocorrelations of two-dimensional ultrasound images of normal and abnormal livers were computed.
It is shown how distributed arithmetic techniques can be applied in parallel-data arithmetic computations to achieve highly regular and efficient VLSI structures on silicon. Two individual arithmetic processor chips are described as examples of the technique. The chips described, which are intended primarily for computation of the FFT butterfly, each contain the functional equivalence of two parallel pipelined multipliers. The first chip is an 8-bit prototype device which has been designed and fabricated on a standard 5-/spl mu/m silicon-gate n-channel MOS process. The second chip is a 16-bit CMOS-SOS design which uses a modified architecture to achieve higher clocking rates and improved versatility in systems use.
Image features such as step edges, lines and Mach bands all give rise to points where the Fourier components of the image are maximally in phase. The use of phase congruency for marking features has significant advantages over gradient based methods. It is a dimensionless quantity that is invariant to changes in image brightness or contrast, hence it provides an absolute measure of the significance of feature points. This allows the use of universal threshold values that can be applied over wide classes of images. This paper presents a new way of calculating phase congruency through the use of wavelets. The existing theory that has been developed for 1D signals is extended to allow the calculation of phase congruency in 2D images. It is shown that for good localization it is important to consider the spread of frequencies present at a point of phase congruency. An effective method for identifying, and compensating for, the level of noise in an image is presented. Finally, it is argued ...
A note on the phase congruence method in image analysis
C A Jacanamejoy
M G Forero
Jacanamejoy, C. A. and Forero, M. G., "A note on the phase congruence method in image analysis," in
[Iberoamerican Congress on Pattern Recognition ], 384-391, Springer (2018).
Split radix'fft algorithm
Duhamel, P. and Hollmann, H., "Split radix'fft algorithm," Electronics letters 20(1), 14-16 (1984).
Study of the phase congruency properties for edge detection in images
Forero, M., Jacanamejoy, C., and Rivera, S., "Study of the phase congruency properties for edge detection
in images," in [Applications of Digital Image Processing XLIV], Tescher, A. G. and Ebrahimi, T., eds., Proc.
SPIE 11842, In-press (2021).
Phase congruency with monogenic filters
C A Jacanamejoy
M G Forero
Jacanamejoy, C. A. and Forero, M. G., "Phase congruency with monogenic filters." Available at https:
// www. researchgate. net/ publication/ 337915149_ Phase_ Congruencyzip (2018).